Consider the transmission scheme for delivering to each of two recipients independently chosen data secretly. It is desirable not to have any assumption on the relationship among the secret decryption keys of recipients. Without any assumption on it, the trivial scheme is to send the concatenation of independently encrypted data for two recipients as the ciphertext. In this scheme, each recipient can separate the ciphertext for him from the entire ciphertext, called recipient-own ciphertext. This paper aims to realize a multiplex transmission in the sense that neither recipient can separate the recipient-own ciphertext from the ciphertext while each recipient can obtain the data to be delivered. If the multiplex transmission scheme is used, each recipient cannot deny that the transmission is done not only for him but also someone. To realize the multiplex transmission, we use the pairing and linear map on elliptic curves. In the proposed scheme, anyone can check whether the delivered values are same or not. Compared with the trivial scheme, the length of the ciphertext and the size of secret decryption key is almost the same and the overhead on the size of public encryption key is feasible while the complexity on decryption increases.